The definition of the inversion symmetry operator I that it transforms a vector into a different vector of same magnitude but antiparallel orentation. This can be written in many ways, e.g. I(r) = -r, or r --> -r, where r is a vector. All "naked" Bravais lattices have inversion symmetry (=they are invariant under inversion symmetry).

Special symmetry elements in 2D are mirror axes and 60, 90 or 180deg rotation symmetry.

The definition of the inversion symmetry operator I that it transforms a vector into a different vector of same magnitude but antiparallel orentation. This can be written in many ways, e.g. I(r) = -r, or r --> -r, where r is a vector. All "naked" Bravais lattices have inversion symmetry (=they are invariant under inversion symmetry).

Special symmetry elements in 2D are mirror axes and 60, 90 or 180deg rotation symmetry.

Time reversal inverts linear momentum (p) and therefore angular momentum, L. It also inverts the spin, S and therefore the magnetic moment.

In a magnetically ordered material, there are well-defined expectation values of the magnetic moment. For example, in a ferromagnet there is a macroscopically observable magnetic moment. Time reversal inverts that.

One approach to systematically investigate the possible arrangements of magnetic moments is the classification into 1651 Shubnikov groups (black-and-white space groups) that are an extension of the 230 crystallographic space groups. Here one moment direction is represented by the color white, and the opposite by black. Time reversal exchanges black and white. Depending on the moment direction, this may also happen for some "normal" space group operations, e.g. a 180-deg rotation about an axis that is perpendicular to the moment direction.